Quantum entanglement is not only a fundamental concept in quantum mechanics but also an essential resource in quantum communication and quantum computing technologies such as quantum teleportation, quantum key distribution and quantum dense coding. There have been many suggestions and experimental realizations of generating entangled states of atoms, ions or phtons. Recently developed cavity QED techniques enable various experiments dealing with single photons and single atoms.
In this work, we propose a scheme to generate a maximally entangled state of two λ-type three level atoms interacting with a cavity photon. In this scheme, the total state of the cavity field and two atoms collapses either to the desired entangled state or to the initial state. By detecting the polarization of the photon leaking out of the cavity one can determine whether the desired entangled state has benn generated or not. With a feedback channel, one can make the probability of success approach unity.
As a specific example for realization of the proposed scheme, we consider the cesium (Cs) hyperfine levels such as ($6S_{1/2},F_g=3$) (as ground state) and ($6P_{1/2},F_e=3$) (as excited state). The realization of this scheme depends on the availability of the proper trapping potential in the cavity and cooling techniques to cool down the atomic thermal motions. A FORT (far -off resonance trapping) beam can be used to make the trapping potential for the atoms, and the Lamb-Dicke condtion for the trapping potential and temperature of the atoms should be satisfied to generate a pure entangled state. One should have a trapping potential whose trapping depth is deeper than several KHz, and the atoms must be cooled down ~10$\mu$K. These conditions can be met by recent or near future cavity QED techniques.
